What is derivative of (arcsin(x))^(2)?

1 Answer
Apr 23, 2015

y=(arcsinx)^2

y^(1/2)=arcsinx

ln(y^(1/2))=ln(arcsinx)

1/2*lny=ln(arcsinx)

1/2*1/y*(dy)/(dx)=1/(arcsinx*sqrt(1-x^2))

2y*1/(2y)*(dy)/(dx)=2y*1/(arcsinx*sqrt(1-x^2))

(dy)/(dx)=(2(arcsinx)(arcsinx))/((arcsinx)*sqrt(1-x^2))

(dy)/(dx)=(2arcsinx)/(sqrt(1-x^2))